To determine how many tickets you can purchase with your family's budget of $685, we first need to set up the inequality based on the costs involved.
Let \( t \) be the number of tickets.
Each ticket costs $125, and there is an online processing fee of $5.75 per ticket. There is also a $20 parking fee.
The total cost for \( t \) tickets can be expressed as: \[ \text{Total Cost} = 125t + 5.75t + 20 \]
This simplifies to: \[ \text{Total Cost} = (125 + 5.75)t + 20 = 130.75t + 20 \]
Now, we need to set up the inequality: \[ 130.75t + 20 \leq 685 \]
Next, we will solve the inequality for \( t \):
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Subtract 20 from both sides: \[ 130.75t \leq 685 - 20 \] \[ 130.75t \leq 665 \]
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Divide both sides by 130.75 to solve for \( t \): \[ t \leq \frac{665}{130.75} \approx 5.08 \]
Since \( t \) must be a whole number (you can't purchase a fraction of a ticket), the maximum number of tickets you can purchase is 5.
Now, let's check if you can afford 5 tickets:
Calculating the total cost for 5 tickets: \[ \text{Total Cost for 5 tickets} = 130.75 \times 5 + 20 = 653.75 + 20 = 673.75 \]
Now compare $673.75 with $685: Since $673.75 is less than $685, you can afford 5 tickets.
So, the correct response includes the inequality and confirms that you can purchase the tickets: \[ \text{Answer: } 130.75t + 20 \leq 685, \text{ and yes, you can purchase the tickets.} \]
Therefore, the best option from your choices is: "125t + 5.75t + 20 ≤ 685, and yes, you can purchase the tickets."
1 answer